Trait/Object

algebra.lattice

Logic

Related Docs: object Logic | package lattice

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trait Logic[A] extends BoundedDistributiveLattice[A]

Logic models a logic generally. It is a bounded distributive lattice with an extra negation operator.

The negation operator obeys the weak De Morgan laws:

For intuitionistic logic see Heyting For fuzzy logic see DeMorgan

Self Type
Logic[A]
Linear Supertypes
Known Subclasses
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Inherited
  1. Logic
  2. BoundedDistributiveLattice
  3. DistributiveLattice
  4. BoundedLattice
  5. BoundedJoinSemilattice
  6. BoundedMeetSemilattice
  7. Lattice
  8. MeetSemilattice
  9. JoinSemilattice
  10. Serializable
  11. Serializable
  12. Any
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Abstract Value Members

  1. abstract def and(a: A, b: A): A

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  2. abstract def getClass(): Class[_]

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    Definition Classes
    Any
  3. abstract def join(lhs: A, rhs: A): A

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    Definition Classes
    JoinSemilattice
  4. abstract def meet(lhs: A, rhs: A): A

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    Definition Classes
    MeetSemilattice
  5. abstract def not(a: A): A

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  6. abstract def one: A

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    Definition Classes
    BoundedMeetSemilattice
  7. abstract def or(a: A, b: A): A

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  8. abstract def zero: A

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    Definition Classes
    BoundedJoinSemilattice

Concrete Value Members

  1. final def !=(arg0: Any): Boolean

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    Definition Classes
    Any
  2. final def ##(): Int

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    Definition Classes
    Any
  3. final def ==(arg0: Any): Boolean

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    Definition Classes
    Any
  4. def asCommutativeRig: CommutativeRig[A]

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    Return a CommutativeRig using join and meet.

    Return a CommutativeRig using join and meet. Note this must obey the commutative rig laws since meet(a, one) = a, and meet and join are associative, commutative and distributive.

    Definition Classes
    BoundedDistributiveLattice
  5. final def asInstanceOf[T0]: T0

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    Definition Classes
    Any
  6. def dual: BoundedDistributiveLattice[A]

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    This is the lattice with meet and join swapped

    This is the lattice with meet and join swapped

    Definition Classes
    BoundedDistributiveLatticeBoundedLatticeLattice
  7. def equals(arg0: Any): Boolean

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    Definition Classes
    Any
  8. def hashCode(): Int

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    Definition Classes
    Any
  9. final def isInstanceOf[T0]: Boolean

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    Definition Classes
    Any
  10. def isOne(a: A)(implicit ev: Eq[A]): Boolean

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    Definition Classes
    BoundedMeetSemilattice
  11. def isZero(a: A)(implicit ev: Eq[A]): Boolean

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    Definition Classes
    BoundedJoinSemilattice
  12. def joinPartialOrder(implicit ev: Eq[A]): PartialOrder[A]

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    Definition Classes
    JoinSemilattice
  13. def joinSemilattice: BoundedSemilattice[A]

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  14. def meetPartialOrder(implicit ev: Eq[A]): PartialOrder[A]

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    Definition Classes
    MeetSemilattice
  15. def meetSemilattice: BoundedSemilattice[A]

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  16. def nand(a: A, b: A): A

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  17. def nor(a: A, b: A): A

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  18. def nxor(a: A, b: A): A

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  19. def toString(): String

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    Definition Classes
    Any
  20. def xor(a: A, b: A): A

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Inherited from BoundedDistributiveLattice[A]

Inherited from DistributiveLattice[A]

Inherited from BoundedLattice[A]

Inherited from BoundedJoinSemilattice[A]

Inherited from BoundedMeetSemilattice[A]

Inherited from Lattice[A]

Inherited from MeetSemilattice[A]

Inherited from JoinSemilattice[A]

Inherited from Serializable

Inherited from Serializable

Inherited from Any

Ungrouped